{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\newcommand{\\IR}{\\mathbb R}\n",
    "\\newcommand{\\d}{\\mathrm d}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Linear Classifiers (logistic regression and GDA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (a)\n",
    "\n",
    "The loss function is \n",
    "$$ J(\\theta) = -\\frac 1m \\sum_{i=1}^m y^{(i)}\\log(h_\\theta(x^{(i)}) + (1-y^{(i)}) \\log(1- h_\\theta(x^{(i)}))$$\n",
    "\n",
    "where $y^{(i)}\\in \\{0,1\\}, ~ h_\\theta(x) = g(\\theta^Tx) = g(x^T\\theta)$ and $g(z)= 1/(1+e^{-z})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that $g'(z) = (1-g(z))g(z)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $p(\\theta) :=\\log(h_\\theta(x))$ for some vector $x$ of the same shape as $\\theta$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then by the chain rule the Jacobian of $p$ at $\\theta$ is\n",
    "$$ \\d_\\theta p(\\theta) = \\frac 1{h_\\theta(x))}g'(x^T\\theta)x^T = (1-g(x^T\\theta))x^T$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Taking the transpose we get the gradient \n",
    "$$ \\nabla_\\theta p(\\theta) = x(1-g(x^T\\theta))$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Differentiating again gives the Hessian:\n",
    "$$ \\nabla_\\theta^2 p(\\theta) = x(-g'(x^T\\theta))x^T = -g'(x^T\\theta)xx^T,$$\n",
    "which is negative semidefinite because $g'$ is positive by monotony of $g$ and $xx^T$ is positive semi-definite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly for $q(\\theta) := \\log(1-h_\\theta(x))$ we have \n",
    "$$ \\nabla_\\theta q(\\theta) = -xg(x^T\\theta)$$\n",
    "and \n",
    "$$ \\nabla^2_\\theta q(\\theta) = -g'(x^T\\theta)xx^T$$\n",
    "which is also negative semidefinite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By linearity we conclude that the Hessian of $J$ has to be positive semidefinite.\n",
    "\n",
    "Since we will need it for part (b), let's spell out the gradient and Hessian of $J$:\n",
    "\n",
    "$$ \\begin{align*}\n",
    "\\nabla_\\theta J(\\theta) &= \n",
    "-\\frac 1m \\sum_{i=1}^m x^{(i)} y^{(i)}(1-g(\\theta^Tx^{(i)})) - x^{(i)}(1-y^{(i)})g(\\theta^Tx^{(i)})\\\\\n",
    "&= -\\frac 1m \\sum_{i=1}^m x^{(i)}(y^{(i)}-g(\\theta^Tx^{(i)}))\\\\\n",
    "&= -\\frac 1m \\sum_{i=1}^m x^{(i)}(y^{(i)}-h_\\theta(x^{(i)}))\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align*}\n",
    "\\nabla_\\theta^2 J(\\theta) &= \\frac 1m \\sum_{i=1}^m x^{(i)}(x^{(i)})^T g'(\\theta^Tx^{(i)})\\\\\n",
    "&= \\frac 1m \\sum_{i=1}^m x^{(i)}(x^{(i)})^T h_\\theta(x^{(i)})(1-h_\\theta(x^{(i)}))\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import src.util as util\n",
    "from src.linear_model import LinearModel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the datasets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dataset:\n",
    "    def __init__(self, train_path, eval_path):\n",
    "        self.x_train, self.y_train = util.load_dataset(train_path, add_intercept=False)\n",
    "        self.x_val, self.y_val = util.load_dataset(eval_path, add_intercept=False)\n",
    "        self.x_train_intercept, self.y_train_intercept = util.load_dataset(train_path, add_intercept=True)\n",
    "        self.x_val_intercept, self.y_val_intercept = util.load_dataset(eval_path, add_intercept=True)\n",
    "        \n",
    "ds1 = Dataset('data/ds1_train.csv', 'data/ds1_valid.csv')\n",
    "ds2 = Dataset('data/ds2_train.csv', 'data/ds2_valid.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at the two training sets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.myplot(ds1.x_train, ds1.y_train)\n",
    "util.myplot(ds2.x_train, ds2.y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement functions to compute $h_\\theta$, and the gradient and hessian of the loss function $J(\\theta)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def h(theta, x):\n",
    "    \"\"\"vectorized implementation of h_theta(x)\n",
    "    Args:\n",
    "        theta: Shape (n,)\n",
    "        x: Shape (m,n)\n",
    "    \n",
    "    Returns:\n",
    "        numpy array of shape (m,)\n",
    "    \"\"\"\n",
    "    return 1/(1+np.exp(-np.dot(x,theta)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient(x,y, theta):\n",
    "    \"\"\"\n",
    "    Args:\n",
    "        x: numpy array of shape (m,n)\n",
    "        y: numpy array of shape (m,)\n",
    "        theta: numpy array of shape (n,)\n",
    "        \n",
    "    \"\"\"\n",
    "    m, = y.shape\n",
    "    return -1/m * np.dot(x.T, y - h(theta, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hessian(x,y, theta):\n",
    "    \"\"\"\n",
    "    Args:\n",
    "        x: numpy array of shape (m,n)\n",
    "        y: numpy array of shape (m,)\n",
    "        theta: numpy array of shape (n,)\n",
    "        \n",
    "    \"\"\"  \n",
    "    m, = y.shape\n",
    "    htx = np.reshape(h(theta,x), (-1,1))\n",
    "    return 1/m * np.dot(x.T, x*htx*(1-htx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define our logistic regression model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LogisticRegression(LinearModel):\n",
    "    \"\"\"Logistic regression with Newton's Method as the solver.\n",
    "\n",
    "    Example usage:\n",
    "        > clf = LogisticRegression()\n",
    "        > clf.fit(x_train, y_train)\n",
    "        > clf.predict(x_eval)\n",
    "    \"\"\"\n",
    "\n",
    "    def fit(self, x, y):\n",
    "        \"\"\"Run Newton's Method to minimize J(theta) for logistic regression.\n",
    "\n",
    "        Args:\n",
    "            x: Training example inputs. Shape (m, n).\n",
    "            y: Training example labels. Shape (m,).\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        def nexttheta(theta):\n",
    "            grad = gradient(x,y,theta)\n",
    "            H = hessian(x,y,theta)\n",
    "            H_inv = np.linalg.inv(H)\n",
    "            return theta - np.dot(H_inv, grad)\n",
    "        \n",
    "        \n",
    "        m,n = x.shape\n",
    "        theta_prev = np.zeros(n)\n",
    "        theta_next = nexttheta(theta_prev)\n",
    "        \n",
    "        while np.linalg.norm(theta_prev - theta_next, 1) > self.eps:\n",
    "            theta_prev = theta_next\n",
    "            theta_next = nexttheta(theta_prev)\n",
    "            \n",
    "        self.theta = theta_next\n",
    "        \n",
    "        \n",
    "        # *** END CODE HERE ***\n",
    "\n",
    "    def predict(self, x):\n",
    "        \"\"\"Make a prediction given new inputs x.\n",
    "\n",
    "        Args:\n",
    "            x: Inputs of shape (m, n).\n",
    "\n",
    "        Returns:\n",
    "            Outputs of shape (m,).\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        return (x @ self.theta) >= 0\n",
    "        # *** END CODE HERE ***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a classifier and train it on our training data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "logreg1 = LogisticRegression()\n",
    "logreg1.fit(ds1.x_train_intercept, ds1.y_train_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's plot the decision boundary on the training set and on the validation set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for dataset1: [-6.26018491  2.47707251 -0.0299125 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"theta for dataset1:\", logreg1.theta)\n",
    "util.myplot(ds1.x_train, ds1.y_train, logreg1.theta)\n",
    "util.myplot(ds1.x_val, ds1.y_val, logreg1.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's do the same for dataset2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for dataset2: [ 2.38425454  3.6371206  -3.81234337]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "logreg2 = LogisticRegression()\n",
    "logreg2.fit(ds2.x_train_intercept,ds2.y_train_intercept)\n",
    "\n",
    "print(\"theta for dataset2:\", logreg2.theta)\n",
    "util.myplot(ds2.x_train, ds2.y_train, logreg2.theta)\n",
    "util.myplot(ds2.x_val, ds2.y_val, logreg2.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (c)\n",
    "\n",
    "By Bayes' rule we have"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align*}\n",
    "p(y=1\\mid x) &= \\frac{p(y=1,x)}{p(x)}\\\\\n",
    "&= \\frac{p(y=1)p(x\\mid y=1)}{p(x\\mid y=1)p(y=1) + p(x\\mid y=0)p(y=0)}\\\\\n",
    "&= \\frac{1}{1+\\frac{p(x\\mid y=0)p(y=0)}{p(x\\mid y=1)p(y=1)}}\\\\\n",
    "&= \\frac {1}{ 1 + \\exp\\left(\\color{red}{-\\frac {1}{2}(x-\\mu_0)^T\\Sigma^{-1}(x-\\mu_0)}+\\color{blue}{\\frac {1}{2}(x-\\mu_1)^T\\Sigma^{-1}(x-\\mu_1)}\\right)\\frac {1-\\phi}{\\phi}}\\\\\n",
    "&= \\frac {1}{1+ \\exp\\left(\n",
    "\\color{red}{-\\frac {1}{2} x^T\\Sigma^{-1}x +\\mu_0^T \\Sigma^{-1}x -\\frac {1}{2} \\mu_0^T\\Sigma^{-1}\\mu_0} \n",
    "+ \\color{blue}{\\frac {1}{2} x^T\\Sigma^{-1}x -\\mu_1^T \\Sigma^{-1}x +\\frac {1}{2} \\mu_1^T\\Sigma^{-1}\\mu_1}\\right)\\frac {1-\\phi}{\\phi}}\\\\\n",
    "&= \\frac{1}{1+\\exp\\left((\\mu_0-\\mu_1)^T\\Sigma^{-1}x  -\\frac {1}{2} \\mu_0^T\\Sigma^{-1}\\mu_0 + \\frac {1}{2} \\mu_1^T\\Sigma^{-1}\\mu_1\\right)\\frac {1-\\phi}{\\phi}}\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we can take $\\theta = -\\Sigma^{-1}(\\mu_0-\\mu_1)$ and $\\theta_0= \\frac {1}{2} \\mu_0^T\\Sigma^{-1}\\mu_0 - \\frac {1}{2} \\mu_1^T\\Sigma^{-1}\\mu_1 - \\log\\frac {1-\\phi}{\\phi}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (d)\n",
    "\n",
    "Let's unpack the definition of $\\ell$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ \\begin{align*}\n",
    "\\ell(\\phi,\\mu_0,\\mu_1,\\Sigma) &= \\sum_{i=1}^m \\left( \\log p(x^{(i)}\\mid y^{(i)}; \\mu_0,\\mu_1,\\Sigma) + \\log p(y^{(i)}; \\phi) \\right) \\\\\n",
    "&= -m \\log\\left((2\\pi)^{n/2}\\lvert \\Sigma \\rvert^{1/2}\\right)\\\\\n",
    "&\\phantom{=} -\\frac {1}{2}\\sum_{i=1}^m 1\\{y^{(i)}=0\\} \\left( (x^{(i)}-\\mu_0)^T\\Sigma^{-1} (x^{(i)}-\\mu_0) + \\log (1-\\phi)\\right)\\\\\n",
    "&\\phantom{=} -\\frac {1}{2}\\sum_{i=1}^m 1\\{y^{(i)}=1\\} \\left( (x^{(i)}-\\mu_1)^T\\Sigma^{-1} (x^{(i)}-\\mu_1) + \\log \\phi\\right)\\\\\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the maximum of $\\ell$, we have $\\d \\ell =  (\\d_\\phi \\ell, \\d_{\\mu_0}\\ell, \\d_{\\mu_1}\\ell, \\d_{\\Sigma}\\ell)= 0$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For readability let's introduce $P:=\\sum_{i=1}^m 1\\{y^{(i)}=1\\}$. We then have\n",
    "$$\\begin{align*} \n",
    " 0 &= -2\\d_\\phi \\ell = \\sum_{i=1}^m 1\\{y^{(i)}=0\\}\\frac 1{\\phi-1} + \\sum_{i=1}^m 1\\{y^{(i)}=1\\}\\frac 1\\phi\\\\\n",
    " &= (m-P)\\frac 1{\\phi -1} + P \\frac 1 \\phi,\n",
    "\\end{align*}$$\n",
    "which can be rearranged to\n",
    "$$ \\phi = \\frac Pm = \\frac 1m\\sum_{i=1}^m 1\\{y^{(i)}=1\\},$$ \n",
    "as claimed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we have \n",
    "$$\\begin{align*} \n",
    "0&= \\d_{\\mu_0}\\ell \\\\\n",
    "&= \\sum_{i=1}^m 1\\{y^{(i)}=0\\} (x^{(i)}- \\mu_0)^T\\Sigma^{-1},\n",
    "\\end{align*}$$\n",
    "which is equivalent to \n",
    "$$ \\mu_0 = \\frac{\\sum_{i=1}^m 1\\{y^{(i)}=0\\} x^{(i)}}{\\sum_{i=1}^m 1\\{y^{(i)}=0\\} }.$$\n",
    "\n",
    "The formula\n",
    "$$ \\mu_1 = \\frac{\\sum_{i=1}^m 1\\{y^{(i)}=1\\} x^{(i)}}{\\sum_{i=1}^m 1\\{y^{(i)}=1\\} }$$\n",
    "is derived similarly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now assume that $n=1$, so in particular $\\Sigma \\in \\IR$ and every vector equals its own transpose. Then\n",
    "\n",
    "$$\\begin{align*} \n",
    "0&= \\d_\\Sigma \\ell\\\\\n",
    "&= -\\frac m{2\\Sigma}\\\\\n",
    "&\\phantom{=} +\\frac {1}{2}\\sum_{i=1}^m 1\\{y^{(i)}=0\\}  (x^{(i)}-\\mu_0)^T\\Sigma^{-2} (x^{(i)}-\\mu_0)\\\\\n",
    "&\\phantom{=} +\\frac {1}{2}\\sum_{i=1}^m 1\\{y^{(i)}=1\\}  (x^{(i)}-\\mu_1)^T\\Sigma^{-2} (x^{(i)}-\\mu_1),\n",
    "\\end{align*}$$\n",
    "\n",
    "which simplifies to \n",
    "\n",
    "$$ \\Sigma = \\frac 1m \\sum_{i=1}^m (x^{(i)}-\\mu_{y^{(i)}}) (x^{(i)}-\\mu_{y^{(i)}})^T$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GDA(LinearModel):\n",
    "    \"\"\"Gaussian Discriminant Analysis.\n",
    "\n",
    "    Example usage:\n",
    "        > clf = GDA()\n",
    "        > clf.fit(x_train, y_train)\n",
    "        > clf.predict(x_eval)\n",
    "    \"\"\"\n",
    "\n",
    "    def fit(self, x, y):\n",
    "        \"\"\"Fit a GDA model to training set given by x and y.\n",
    "\n",
    "        Args:\n",
    "            x: Training example inputs. Shape (m, n).\n",
    "            y: Training example labels. Shape (m,).\n",
    "\n",
    "        Returns:\n",
    "            theta: GDA model parameters.\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        # Find phi, mu_0, mu_1, and sigma\n",
    "        # Write theta in terms of the parameters\n",
    "        \n",
    "        m,n = x.shape\n",
    "        y_vec = np.reshape(y,(-1,1))\n",
    "        \n",
    "        phi= 1/m * np.sum(y)\n",
    "        mu_0 = np.sum(x*(1-y_vec), axis= 0) / np.sum(1-y)\n",
    "        mu_1 = np.sum(x*y_vec, axis=0) / np.sum(y)\n",
    "        mu_x = y_vec*mu_1 +(1-y_vec)*mu_0 # shape (m,n)\n",
    "        x_norm = x-mu_x\n",
    "        sigma = 1/m * np.dot(x_norm.T, x_norm)\n",
    "        \n",
    "        sigma_inv = np.linalg.inv(sigma)\n",
    "        \n",
    "        theta = -np.dot(sigma_inv,mu_0 - mu_1)\n",
    "        theta0 = np.array([1/2* mu_0 @ sigma_inv @ mu_0 -1/2* mu_1 @ sigma_inv @ mu_1 -np.log((1-phi)/phi)])\n",
    "        self.theta = np.concatenate((theta0, theta))\n",
    "        \n",
    "        return self.theta\n",
    "        # *** END CODE HERE ***\n",
    "\n",
    "    def predict(self, x):\n",
    "        \"\"\"Make a prediction given new inputs x.\n",
    "\n",
    "        Args:\n",
    "            x: Inputs of shape (m, n).\n",
    "\n",
    "        Returns:\n",
    "            Outputs of shape (m,).\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        x_intercept = util.add_intercept(x)\n",
    "        #return 1/ (1+ np.exp(-x_intercept @ self.theta))\n",
    "        return x_intercept @ self.theta >= 0\n",
    "        # *** END CODE HERE\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's train a GDA classifier for dataset 1 and plot the learned decision boundary on the training and the validation set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for dataset1: [-6.17158405  2.22055506 -0.01763375]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gda1 = GDA()\n",
    "gda1.fit(ds1.x_train, ds1.y_train)\n",
    "\n",
    "util.myplot(ds1.x_train,ds1.y_train, gda1.theta)\n",
    "util.myplot(ds1.x_val,ds1.y_val, gda1.theta)\n",
    "print(\"theta for dataset1:\",gda1.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same for dataset 2:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for dataset2 [ 2.50874989  3.76951271 -3.94657107]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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vfc8Gg02Z4kowWLzohQ8+COaa8rBeudqRFvgclOkSwXiF0hC97M6Jq06dECnaqxtXJxxjIELI4gWDvf66q8Fg8ZY+jh7t0yt2u+DURVN+pz14lbJ4FxmdP/R8nv3HsxlfPOSkROcLiguLo8bo+x79K6/YJSmrVtnbY8bAbbfBHntk5eUTLX0MQy87qBL14HXTbZWySEF04kpQt8U7XxCraLvZo8/oytl16+Dqq20QGNgcmbvvzvo0ecfSx3k1FF5ayfDX1lC0rIjyvaqovrt8Ry+7rMz/M/hcoQVepaV8SLnnBT2ZoplK0S4qLIo5g8/0PELHTxGR1g+Q+M+wpQUefNA2r7/80ubFVFba2x5kx9TWwu0v1dD9zAoaTdt7uXl9BdfeCTeNLqesLDhtmlygPXgVSLH65ec9eR79pvaL6pmnckGUW+mVacUqrFgBP/iBzWX/8su2YLBJkzwr7qNGQcHISraZ6PdC9yZqvrDvJay97KDSAq8CKVbRBNiweUPUidFUirZbFy2l1PppaoJrrrHRAosW2WCwxx6DF16A/fbLaByZiJyUXLel6/fitxUzuUxbNCqQEvXFI7Pj9m2kZPvfbrSekm79LFgAl10GDQ02COySS6CqCvr0cXQ86YgU7KJl7rSxlDt0Bq8CqauC0v4A4FRyZLq6/BTxySdw1ln24qSGBjt7/8tf7MVLPiju7bnVxlLu0AKvAilWoWnPjRlluhdBxW39DPoJ3HGHDQZ74gl7gdL06bYfcuSRQPQFRpHft9/bNdv7vPoqe0d1SdfBq8Cqqa9h/HPj2bB5Q9T9Tm8uEnktRzcxWbwYLr7YXn0KNs7wjjtg332jHtb+ikuAk0+2iQTPPGNvjxplW/bbt2vfO1dpFo1yjJ8u5S8fUs76ieuZdeYsR2aUid6bY9sdNjbaPvuRR9riXlQETz9tr+/vUNyhbVVK5CrS/Hx7HvbBB9uK+y23hCfmNl4kQjY/pYSKiPjm67DDDhPlX7OWz5KCqgLhRnZ8FVQVyKzls9J+vuLbi8XcaKT49uK0n8cJXb03c6OJ+l7ky9xoknuBlhaR2bNF9tpLBETy80UmThT55pukfnzSJPtjkyaJjBljf3/ssSL9+oksXJjuu/afhQuj31PH26ozoE7i1FSdwaukOblpd6a5L/Fm2+l+wujqvaWynr7TLPSDD9hw5EnRwWDvvANTplD7du8uZ6ftUw/vuMNO+I891sbPnHRSuC4oav+JJUjZNn6lBV4lzclL+TM5WMQ7OGSy6UhX7y2V1SORYK5XXtgCVVU0HzCY3Re/wH967cYVO1dTe5MNBktmr9KOWerG2H77smU2imbWLHteNkz8vBtU0GiBV0lLd5u8WDI5WMQ7OFQvqU77oNHVe0tl9UhZGbxY+Sr/dcrBcN115G/9D1/8aAw9G1Yx8umfM2p0XtKz0/aph4sX21ltfr79MPDwwzZrbNIkb2Ju3eqX50JOe7ZogVdJc3INdCYHi3gHgWZpTvrxNfU19JvaDzPZYCYb1jetp0d+j6jHdHxvSa2nX78eLriAQ64YxnebV/E3vsuD573MXi8+DHvskfLsdOLEtsdMnGhn7/Pm2f2zAa68EubP9yYaIF6EcCYnfHMlpz1bEhZ4Y8yuxpjvxLj/IPeGpLIp2Z51JNiraVsT+SYfIKMVK5kcLOIdBPJM7H/OHR9fU1/DhfMujFpeuWnbJrY2b93xHCm/t5YWeOABm/T40EM0d9+JWwsmM/ua5Ux8/vioIpjJ7LR9wY/wKhrAjX55ruS0Z0vcdfDGmFHADGAt0B24QEQWt35vqYgc6vRgdB18diW7ttvxNeDtnjcSIdC3V1/AbgreVZxArPF0z+tOi7R0msX3yO/BA6c9EPVc8XLf035vK1bYNe2LFtn3cNgPOenDu7j1if2j9iSNLGkMwl6lqdAseG+luw7+WuAwETkYuBB4xBhzZuQ5HR6jSlMm69KTPdGZ7OM6juWSBZckHFuk5fHImY+weftmNmzekNTJ0Vj98F132jVmi2aXHrtQPqQ8ql/cVZ8/6ZVBsYLBHn2U+85+cUdxh7ZZ6Esvtc1Ga2ujZ6dBXevtl365rp+PLdEMvl5EhrS7vTcwH3gIO5vXGbzHMp1Z503Oi7lZtsHwyJmP7Jhdx9tQ22BouaEl7lg6ijc2J3ZSSvReWm5oiZotX7gs8Qy+/c/F9eyzcOmlbcFgF18MN9+cVHZMx5l7UGfyfnoffhpLtqU7g9/Yvv8uIp8Dw4DTgANTePF8Y8w7xpj5yf6MSk6m69Lj9bL79uobtdwwmZ+PF9/bcWznzz2/08zcieWXXZ20bd8vPuTfVbC9e1rPx6efwtlnwymn2OI+dKgNBrvrrqSDwbK91tut2a2f+uW6fj62RAV+LJBnjDkgcoeIbAROBH6WwmuMB1amNzyVSKaFMd6JTqDLYt3xhGiyr9kszZ3aL04sv0zmpG1kBcu8m8o5Pe9Bdu+1e8zninmyt7nZXmU0cCA8/nhbMFhd3Y5gsFRkc623G6tdwF8nfCOvrevno8Ut8CKyTET+AcwxxvzSWL2A6cAlyTy5MWYf4BTgPkdGq6JkWhjjre3+cvOXcX8m3hrwVIpxx08ZTiy/TGadevt+8aK7yvnT4euRG6TrLJu6OjjiCJgwAb75Bk4/HVauhCuugG7pbamQzd51rsxu/XI+wFfiZRhEvoDewEzgL8B7wDVAXlc/1/qzjwOHYVs78+M8pgKoA+qKiopcy2sII6ezYSKKby+OmbtSfHtxSmNJ9NUxw8XtXJq0Mk6++krksstEjLHhL0VFIk895c1YHNA+zyZscjnDhgyzaLYBm4FeQE/gIxFJcPbJMsaMANaKyJIuDjDVIlIqIqX9+/dPYjgqwq1s7nRm1LHGMrZ07I418x11nPG7vSlHSv1iEfvNQYNg5kzIy4Orr4b334eRI7M7FoeEfXbrp/MBvhKv8kvbDHsZcBN2LfxewFPA40n83C3AJ0AD8AXQBMxK9DOaJukfTs2o3fqU4ZoPPhA58UQ71QWRo48WWbbM61FlJNHsdsqUzrPcyP0qGEgwg0+mwJfGuG9MVz/X4fHDiNOiaf+lBT6ckjlYeB4dvGWLSFWVSM+e9r9Fnz4i1dUizc3ZHYcLEhXxXG5thEWiAp+VHZ2MMcOAq0RkRKLH6Tr43OTWlbJJe/VVu+xiZetir/POg2nTYI893H9tH4isqhk71rZvYp2AnTrVrrppf39trW2B6E5S3vJ8RycReaWr4q5yl5M58ylZvx4uvBCGDbPF/bvfhZdfhkceyZniDsktL3RrqaVyl6ZJqk6c3pavq+dzMmc+Ke2Dwf7wB9hpJ5g8GZYvh+OPd+c1fSyZE7C5stQybNJbxKtCq2O7JJILA6S9z2lXz1dUWBQzOiCdnPkurVhhp6mvv25v//CH9irU/fd3/rUCoOMl/WVl8Yt3+5n+pEla3INAZ/AqitPtkmSeL9llmRl9smhqgmuvtcFgr79uWzA1NfDiizlb3CG15YVhX2oZRjqDV1Gcbpck83yRmXwk3CxWXHBGnyyee84Gg330UXQw2G67pfWewiTWCdLITL69VGb6yj90Bq+iZsbJbpqRrGTjFLq60CmdTxZ3VX7K2h+cDSefbIv70KEsufNNpn77bi3uKdILiYJJZ/A5ruPMOFamerrb8oFtv8RaApnq86X0yaK5GX73OypmXEe3po1s79mbblU38cpB4zj7nG7MmZPSSyuSn+krf9EZfI6LF/Obb/IdiT9wKk4h6WC1SLrj+PF0a9rIumNOp7TX+1z/1ZU7ins2ipJuQKH8QAt8wGW6pDHezLhFWhzLhXEiZ6bLE7GNjXD55Tb1cckS2HdfeOop+i+ay8jLirIeIavrxpUfaIEPsEh7JbIxR1db3cXiRBZ7NsT9JDD4XPjTn6KDwa66akcwmFcrP3TduPKDrEQVJEujClLjxFZ3nscEZOLDD+3qmOeft7ePOgruvRcOOgjwxzZuuiG1cpvnUQXKHU4saXQrcjgi3V50wp/butUuczzwQFvc+/Sxhf2NN3YUd8j+yo+OY66ttZtADR+u68aVN3QGH2BOzODdlu4suv3jPutXw5ULKln7nzWM/HwPHn4pn8IPP7MPPO88uO022HNPR8abSahW+zGD3fjJGJg7197WNo1yQ6IZfNKRv9n40rjgxDpG6o6dPzYQWeuRCNpJk1KLol24UGTno2dJ9xsKZPerkfsPZkdOe2PxXiIvveTaWNONz408fvhwkcLC6J/LZs665rznDjLJg8/mlxb4+OJtnDF2/lhvc9STlO52cYXXF8kFpyHretnC/p985PphyHenure9Y7oHpAg/bI2nOe+5Qwt8CKSzT6pfpFsw//rACnm1qG3W/udvI/tfFntPV6elW6QzPTg4yU9jUe5JVOD1JGtAZD1S1yHt+9I33dS2dDDhCcemJlaXX8uh/28ox62Bf/WGc8+EH/0U/tHPPqT9Mk6nLypKd2llWu/VRcnkvKtw0wIfEEFZr95RyitZnnsOBg+m+NFb6Gaa+fvZwzn0il48dhBg7EM6Rh04eVFRJkXab3kttbUwfTqMGRN9oMr0ilq9SjdA4k3tvfjSFk18gdu8OlWffipy9tk72jFy0EEif/mLiCS3X6tT7YiwnJyM/HlMmxb710zaNdrf9xe0Bx8Onm9M7Ybt20V++1uRXXax/xx79xa57TaRbdtSfio/nNxMhRMHk3jPcdJJnQvwmDEiBQXOFGLt7/uHFnjlT3V1Iocd1jZrP+00kdWr03qqoBWcKVM6z6anTUu9ACc7m3bj4Be0A2pYaYFX/tLYKHL55SJ5efaf4L77isybl/bTBbFl0LGFMmaMiDH2drrPFe/g5sbBL2gH1DDTAq+yosuWQ0uLyJw5Invvbf/p5eeLXHWVyMaN7r6uT0WK5LHH2j+OMWPSf654s2k3Dn5BPKCGmRZ4lRUJ/+N/8IFtDEfaMUcdJfLuu56O1w/GjLF/HMcem36RTDSbduPgF9QDalhpgVdZ07HY1L6wReTmm0V69rT/3Pr0EbnnHpHmZq+H6rlp02xbZsyY9Fe4uD2b1mLuf1rgVVZF2gX3nf+ayAEHtM3ay8tFvvjC6+H5wsKFdsFQpOfevifvxCoapwqwtmP8z5MCD/QE3gaWASuAyV39jBb44Fu4UOS7fdfJkqEXthX2/fd3JRgsyII0M9YTqv6WqMC7FhdsjDFAbxH5xhjTHVgEjBeRv8b7GY0LDrbahcKTpz3EtLyr6PH1Blq69+C2btdw5Nxf8YMf9/R6eCoDunGJf3my4UfrweWb1pvdW7/8Ez6vnPX+++z3s2Hc+c2F9Ph6AwwfTt579Ry+4EbeWqbFPducjBPwattD5YB4U3snvoB84F3gG2BKnMdUAHVAXVGRexGwyiWbNolce61I9+62HbPHHiKzZtklkSGXqM0S63sVFfYr1uOd5lTvXHvw/ofXJ1mBPkAtMDjR47QHHzDPPSfy7W+39dovukjkyy9df1m/RDYkKn6xvrfrrtGbgLhdLJ3onQfpXEGu8rzA2zFwA3BVosekU+D98p89p3z6qcioUW2F/aCDRN58Mysv7bfQtURFNNb3sn3CUuMEws+TAg/0B/q0/r4X8DowItHPpFrg/fafPfS2b5e3f/VT+XonIwKyqYeRul+cK7J1a9aGEG/jkz1uKY56XDZnmYmKaKzvZavo6uqX3JCowLuZB783UGuMWQ4sBv4sIvOdfIHKlytp2tYUdV/TtiYqX6508mUUwJIlbDhofw6/9WF22SI8NQAGXiIc13ceNavmZG0Y8TY4WfufNY7kwacq0QnIWN/L1glLv20+orzRza0nFpHlwCFuPT8Ed5ejQPn6a1uNZs5k95YW1uwKl58MTw9s/X7rAbV8SHlWhlNUWMTqxtWd7t+jZxGjRtmdi+6+O3rjDbe0L6JlZfYrchs6f+/008EYmDu38+OdHmuizUd0Z6fc4VqBz4Z4/9n9vstRIIjAE0/A+PHw2WeQn8+0o+GGYbBpp+iHZvOAWjW8iopnKqI+uRV0L2D6KVX8raltrXY2ilhXOzh1/N7o0W2/7/h4p8c7cWLn+yIHFZU7XLvQKR2pXhHmXRUAAAxYSURBVOhUU18T8z979anVWZtRhtJHH8Gll9rt8wCOPBLuvZeS2tNiHlCLC4tpmNCQteHV1NdQ+XIlaxrXUFRYRNXwKv5rfXnWZ/BK+YEnFzplQ/mQcqpPraa4sBiDobiwWIt7JrZuhVtugQMPtMW9sNBWyzffhKFDqRpeRUH3gqgf6bg/ajaUDymnYUIDLTe00DChYUdx136zUtECPYNXDnr9dbj4Ynj/fXv73HPtjs177hn1sFizZ68PqFOn2hOq7WfstbW29RGrVaFUmCSawWuBz3UbNtgq+MAD9vb++8Ndd8EPf+jtuJRSSQltiybsauprKJlRQt7kPEpmlFBTX+Pck4vAH/4AAwbY4t6jB9xwAyxfrsVdqZAI9CqaMOt4Anl142oqnqkAyLwlsnKlbce89pq9ffzxdtY+YEBmz6uU8hWdwfuUKxdxbd4M110HQ4fa4t6/PzzyCLz0khZ3pUJIZ/A+5fhFXM8/b5c+fvihvX3RRXbFzG67pTlCpZTf6Qzep+JdrJXyRVyffQY/+QmcdJIt7kOG2GWP99wTt7g7mSWulPKOFnifynjNeXMzzJwJgwbZheEFBfCb38CSJXD00Ql/9PDDo9eRZzPbRSnlHC3wPpXRRVxLl8JRR8Hll9ssmZEj7YnVq66C7t27/PHIJfSjRtmt2tzKS/Ej/fSiQiVezKQXX7rhR4YaG0XGjRPJy7N5tPvuKzJvXtpPl4tZ4rqDkQoaPIoLVtkiAo8/btsxv/2tjSy88kp7Veppp6X1lLm6D2cuf3pR4aMFPug++ghGjICzz7YnVI88EurqYNo02HnntJ4yTFni6bRcyspsaNmvf21/1eKugkoLfFBt2wa33mqDwZ59ti0Y7I034OCDM3rqrmJwgySdE8a5+ulFhVC83o0XX9qDT9Lrr4sceKDs2BP13HNFPv/c61H5Vipb12kPXgUN2oMPiQ0b4Gc/g2OPhRUrYL/94MUXoaYG9trL69H5ViotlzB9elFK0ySDQAQeftguc1y/3gaD/epXcM010LOn16PzvUhbRjcDUWGUKE1Sowr8buVKW5lefdXe1mCwlCTaN1WLvAo7bdH4VftgsFdf1WCwNKXSctGLnFTYaIH3oxdegMGDoarKrpapqIBVq+C88+wadw8EtfhNnNh5pl5WFnunJ41oUGGjBd5PPv8cRo+GE09sCwZ74w24917o29fToeVC8dOLnFTYaIH3g+Zm+N3vYOBA+OMfbTDY1Kk2GOx73/N6dEDuFD+9yEmFiRZ4ry1datMdL7vMBoOdeqqNGLj66qSCwbIpF4qfXuSkwsS1Am+M2dcYU2uMWWmMWWGMGe/WawXSxo0wYYLtcSxeDPvsA3PnwlNPQXGx16OLKezFL0wRDUqBuzP47cAvRGQQcBRwqTHmABdfLxhE4IknbDDYHXe0BYOtXAmnn+7ZSdSu5ELx04ucVNi4tg5eRD4HPm/9/UZjzErgW8D7br2m7zU02G3znn3W3j7iCHsCNcPsmGxIVPzC0qqJtbImsnZeqSDKypWsxpgS4DVgsIh83eF7FUAFQFFR0WGrV692fTxZt20bTJ8Okyfb9e2FhXY/1IoKyM/3enRKqQBLdCWr6ydZjTE7A08AEzoWdwARqRaRUhEp7d+/v9vDyb5Fi+CQQ2y0wObNcM45dk372LFa3JVSrnK1wBtjumOLe42IPOnma/lOvGCwRx/VYDClVFa4uYrGAPcDK0Vkuluv4zsi8NBDdk37/ffbYLDrr4f6evjRj7wenVIqh7gZNnYMMAaoN8a823rftSLyrIuv6a1Vq+Dii9uCwcrKbDDYwIHejksplZPcXEWzCPDnmj+nbd4MN98MU6bYE6r9+9st8zzMjlFKKY0LztSLL8Ill8AHH9jbP/+53UrP4+wYpZTSqIJ0RYLBfvxjW9wHD7bBYNXVWtxDIqgJmkpFaIFPVbxgsKVLfRMMppyRCwmaKty0RZOKpUvtSdTItesjRsDMmb7NjlGZaZ+gqdv9qSDSGXwyNm6EK66IDgZ78kl4+mkt7iGXCwmaKry0wCciYgv5oEEwY4a974orbJzvGWfoCpkcEPYETRVu2qKJp6HBZrQvWGBvH3EE3HOPjR1QOUE37FZBpzP4jrZts+vZDzjAFvfCQnux0ptvanHPMRofrIIuK2mSySotLZW6ujrvBvDGG/Yk6nvv2dujR8Ptt2t2jFLKtzxNkwyEL7+0Fyh9//u2uH/nO/DCC/DYY1rclVKBldsFXgQefhgGDID77rN7oE6aZIPBTjjB69EppVRGcrfAr1oFxx8P558P69fDsGGwfLndj65XL69HF0WvqFRKpSP3CvzmzXaWftBB8Mor0K+fncUvXOjb1Ee9olIplY7cWiYZ0GAwvaJSKZWO3JjBf/653SqvfTDYokWBCgbTKyqVUqkKd4Fvbm7bcGP2bNtbnzLFZsocc4zXo0uJXlGplEpVeFs077xj17S//ba9PWIE3HknlJR4Oqx06BWVSql0hG8GHwkGKy21xf1b32oLBgtgcQe9olIplZ7wXMkqAnPnwrhx8OmnkJcH48fD5Mmwyy7ODlQppXwi0ZWs4WjRNDTA5ZfD/Pn29uGHw733anaMUiqnBb/AL1hgG9JNTbDrrnDLLXDRRZCf7/XIlFLKU8Ev8KWl0KMHjBwJ06fD3nt7PSKllPKF4Bf4Pfe0G3BoYVdKqSjhWEWjxV0ppToJR4FXSinViWsF3hjzgDFmrTHmPbdeQymlVHxuzuD/AJzo4vMrpZRKwLUCLyKvAV+69fxKKaUS0x68UkqFlOcF3hhTYYypM8bUrVu3zuvhKKVUaHhe4EWkWkRKRaS0f//+Xg9HKaVCw1cXOi1ZsmS9MWa11+No1Q9Y7/UgHBa29xS29wP6noLCT++pON43XEuTNMY8BgzD/kH8C7hBRO535cVcYIypi5fQFlRhe09hez+g7ykogvKeXJvBi8g5bj23Ukqprnneg1dKKeUOLfDxVXs9ABeE7T2F7f2AvqegCMR78tWOTkoppZyjM3illAopLfBKKRVSWuA7CFsKpjFmX2NMrTFmpTFmhTFmvNdjypQxpqcx5m1jzLLW9zTZ6zE5wRiTb4x5xxgz3+uxOMEY02CMqTfGvGuMqfN6PE4wxvQxxjxujFnV+n/qaK/HlIj24DswxhwHfAM8LCKDvR5PpowxewN7i8hSY8wuwBLgdBF53+Ohpc0YY4DeIvKNMaY7sAgYLyJ/9XhoGTHGXAmUAruKyAivx5MpY0wDUCoifrkgKGPGmIeA10XkPmNMD6BARL7yelzx6Ay+g7ClYIrI5yKytPX3G4GVwLe8HVVmxPqm9Wb31q9Az1SMMfsApwD3eT0WFZsxZlfgOOB+ABHZ6ufiDlrgc4oxpgQ4BHjL25FkrrWd8S6wFviziAT9Pc0AJgItXg/EQQK8aIxZYoyp8HowDvhvYB3wYGsr7T5jTG+vB5WIFvgcYYzZGXgCmCAiX3s9nkyJSLOIHAzsAxxhjAlsO80YMwJYKyJLvB6Lw44RkUOBk4BLW9ufQdYNOBS4W0QOATYBv/J2SIlpgc8BrX3qJ4AaEXnS6/E4qfUj8isEe/ewY4CRrT3r2cDxxphZ3g4pcyLyWeuva4G5wBHejihjnwCftPu0+Di24PuWFviQaz0heT+wUkSmez0eJxhj+htj+rT+vhfwQ2CVt6NKn4hcIyL7iEgJMBpYKCLneTysjBhjeree1Ke1jXECEOiVaSLyBfCxMWZA613DAV8vVvBVXLAftE/BNMZ8QsBSMGM4BhgD1Lf2rAGuFZFnPRxTpvYGHjLG5GMnKXNEJBRLC0NkT2CunV/QDXhURJ73dkiOuByoaV1B8yFwocfjSUiXSSqlVEhpi0YppUJKC7xSSoWUFnillAopLfBKKRVSWuCVUiqktMArlQRjzPPGmK/CkvSocoMWeKWS8xvs9QRKBYYWeKXaMcYcboxZ3po537s1b36wiLwMbPR6fEqlQq9kVaodEVlsjHka+F+gFzBLRAJ9ib3KXVrglersJmAx8B9gnMdjUSpt2qJRqrO+wM7ALkBPj8eiVNq0wCvVWTUwCagBpng8FqXSpi0apdoxxvwU2C4ij7amVb5pjDkemAwMBHZuTRn9/yLygpdjVaormiaplFIhpS0apZQKKS3wSikVUlrglVIqpLTAK6VUSGmBV0qpkNICr5RSIaUFXimlQur/ANQ6H+mbTfkPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gda2 = GDA()\n",
    "gda2.fit(ds2.x_train, ds2.y_train)\n",
    "\n",
    "util.myplot(ds2.x_train,ds2.y_train, gda2.theta)\n",
    "util.myplot(ds2.x_val, ds2.y_val, gda2.theta)\n",
    "print(\"theta for dataset2\" ,gda2.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Decision boundaries on dataset 1** (Logistic regression in red, GDA in black):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for logistic regression: [-6.26018491  2.47707251 -0.0299125 ]\n",
      "                theta for GDA: [-6.17158405  2.22055506 -0.01763375]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.myplot(ds1.x_val, ds1.y_val, logreg1.theta, gda1.theta)\n",
    "print(\"theta for logistic regression:\",logreg1.theta)\n",
    "print(\"                theta for GDA:\", gda1.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (g)\n",
    "\n",
    "**Decisionboundaries on dataset 2** (Logistic regression in red, GDA in black):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for logistic regression: [ 2.38425454  3.6371206  -3.81234337]\n",
      "                theta for GDA: [ 2.50874989  3.76951271 -3.94657107]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.myplot(ds2.x_val, ds2.y_val, logreg2.theta, gda2.theta)\n",
    "print(\"theta for logistic regression:\",logreg2.theta)\n",
    "print(\"                theta for GDA:\", gda2.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compare the models, let's compute their accuracies:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(clf, x_val, y_val):\n",
    "    y_pred = clf.predict(x_val)\n",
    "    #print(y_pred)\n",
    "    correct = np.sum(y_pred == y_val)\n",
    "    total = y_val.shape[0]\n",
    "    return correct / total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracies on dataset 1:\n",
      "Logistic regression: 0.9\n",
      "                GDA: 0.83\n",
      "********************************\n",
      "Accuracies on dataset 2:\n",
      "Logistic regression: 0.91\n",
      "                GDA: 0.91\n"
     ]
    }
   ],
   "source": [
    "logreg1_acc = accuracy(logreg1, ds1.x_val_intercept, ds1.y_val)\n",
    "logreg2_acc = accuracy(logreg2, ds2.x_val_intercept, ds2.y_val)\n",
    "gda1_acc = accuracy(gda1, ds1.x_val, ds1.y_val)\n",
    "gda2_acc = accuracy(gda2, ds2.x_val, ds2.y_val)\n",
    "\n",
    "print(\"Accuracies on dataset 1:\")\n",
    "print(\"Logistic regression:\", logreg1_acc)\n",
    "print(\"                GDA:\", gda1_acc)\n",
    "print(\"********************************\")\n",
    "print(\"Accuracies on dataset 2:\")\n",
    "print(\"Logistic regression:\", logreg2_acc)\n",
    "print(\"                GDA:\", gda2_acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So while both logistic regression and GDA seem to have the same performance on dataset 2, GDA performs worse on dataset 1.\n",
    "\n",
    "The reason for this is that dataset 1 doesn't fit the model assumptions of GDA as well as dataset 2, i.e. the data in dataset 1 does not fit well to a multivariate gaussian distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (h)\n",
    "\n",
    "Let's have another look at dataset 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "util.myplot(ds1.x_train, ds1.y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The $x_2$ values of both classes seem to be positive and there seem to be many values close to $0$. Let's transform the data by applying $\\log$ to $x_2$ and leaving $x_1$ unchanged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "transform = lambda x: np.stack((x[:,0], np.log(x[:,1])), axis=1)\n",
    "\n",
    "x_train = transform(ds1.x_train)\n",
    "util.myplot(x_train, ds1.y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks more gaussian. Let's fit a GDA model to the transformed dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gda3 = GDA()\n",
    "gda3.fit(x_train, ds1.y_train)\n",
    "util.myplot(x_train,ds1.y_train, gda3.theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally let's check if we could improve the accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   GDA accuracy on original dataset1: 0.83\n",
      "GDA accuracy on transformed dataset1: 0.95\n"
     ]
    }
   ],
   "source": [
    "x_val = transform(ds1.x_val)\n",
    "gda3_acc = accuracy(gda3,x_val, ds1.y_val)\n",
    "print(\"   GDA accuracy on original dataset1:\", gda1_acc)\n",
    "print(\"GDA accuracy on transformed dataset1:\", gda3_acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a much better fit.\n",
    "\n",
    "Just for fun let's also train a logistic regression model on the transformed dataset and then compare its performance to our new GDA model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "logreg3 = LogisticRegression()\n",
    "x_train_intercept = util.add_intercept(x_train)\n",
    "logreg3.fit(x_train_intercept, ds1.y_train)\n",
    "util.myplot(x_train,ds1.y_train, logreg3.theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic regression accuracy on transformed dataset1: 0.95\n",
      "                GDA accuracy on transformed dataset1: 0.95\n"
     ]
    }
   ],
   "source": [
    "x_val_intercept = util.add_intercept(x_val)\n",
    "logreg3_acc = accuracy(logreg3,x_val_intercept, ds1.y_val)\n",
    "print(\"Logistic regression accuracy on transformed dataset1:\", logreg3_acc)\n",
    "print(\"                GDA accuracy on transformed dataset1:\", gda3_acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta for logistic regression (red): [ 1.96299173  3.56623663 -3.64318719]\n",
      "              theta for GDA (black): [ 1.89345089  3.69641657 -3.71982993]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"theta for logistic regression (red):\", logreg3.theta)\n",
    "print(\"              theta for GDA (black):\",gda3.theta)\n",
    "util.myplot(x_val, ds1.y_val, logreg3.theta, gda3.theta)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
